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Question
D, E, F are the mid-point of the sides BC, CA and AB respectively of ΔABC. Then ΔDEF is congruent to triangle
Options
ABC
AEF
BFD, CDE
AFE, BFD, CDE
Solution
It is given that D, E and Fare the mid points of the sides BC , CA and AB respectively of ΔABC
FE =BD (By mid point theorem)
BD = DC (As it is mid point)
Now in ΔAFE and ΔDFE
FE(Common)
DF = AE (Mid point)
AF = DE (Mid point)
⇒ ΔFED ≅ ΔBFD
⇒ ΔDFE ≅ ΔDCE
Hence (d)
ΔDFE ≅ AFE
≅ BFD
≅ CDE
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